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Trivial modifications are needed, for instance, applications whose tasks execute different code, but have the same input data, or applications in which both the code and the input data is different for all tasks.
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Further modifications are almost inevitable.
Running a piece of non-trivial software without modifications is rarely possible after more than a few years.
Although this algorithm is the optimum method in terms of number of operations, it is in need of non-trivial modifications to be efficiently parallelized on NVIDIA GPUs.
Some modifications were necessary.
By obtaining multiple secondary patents, often for trivial modifications to the original, companies are able to protect their product for decades, preventing production of cheaper generic replicas.
This simple modification is trivial to implement, introduces no instability and improves predictions in all tested cases, even far from stagnation points where this was not expected.
There are plenty of examples of patents being issued for trivial modifications to existing inventions (such as prescription drugs) that allow companies to reap huge profits by extending their exclusive rights to the IP--and also inhibit innovation.
Sometimes, a change in name may be just a trivial modification, but in other occasions it may signify a change in course, focus, or perception about the mission of a journal, its audience and its content.
This weak point is relaxed by a trivial modification.
However, the basic hypothesis-testing framework described below could be used with only trivial modification.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com